The 30-year-old's season was ended in October by a knee injury, after making just six appearances following a £6m move from Wigan.
Kone, who is pleased not be part of Ivory Coast's World Cup squad so that he can continue his recovery over the summer, admitted watching Everton's successful first season under Roberto Martinez was painful.
"Last season was pretty much a non-starter for me so next season is when it starts," he said.
"It is painful to sit in the stands and watch. It is something I never thought would have happened and I look back with a bit of regret.
"Everton have had a fantastic season and the style of play I was watching would suit me down to the ground, which gives me huge motivation to prepare for next season.
"I have to prove my worth and I am ready to take on that challenge. The most important thing is for me to be in the best possible shape I can be.
"I have decided not to go on a big holiday. Instead, I am staying in Europe to work hard over the summer period so I can hit the ground running when pre-season starts in July.
"It is going to mean an awful lot to me to wear that shirt next season because I've not made my mark in the club's history. Hopefully we can make it more successful than the last one has been."